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Preserve the SANY binding of SUBSET against \ and \union. #140

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Merged
muenchnerkindl merged 1 commit into from
Nov 6, 2026
Merged

Preserve the SANY binding of SUBSET against \ and \union. #140

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2 changes: 1 addition & 1 deletion modules/FiniteSetsExtTheorems.tla
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Expand Up @@ -188,7 +188,7 @@ THEOREM ProductSetZero ==
(* bounded by the product of the full set. *)
(*************************************************************************)
THEOREM ProductSetNatSubset ==
ASSUME NEW S \in SUBSET Nat \ {0}, IsFiniteSet(S),
ASSUME NEW S \in SUBSET (Nat \ {0}), IsFiniteSet(S),
NEW T \in SUBSET S
PROVE ProductSet(T) <= ProductSet(S)

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4 changes: 2 additions & 2 deletions modules/FiniteSetsExtTheorems_proofs.tla
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Expand Up @@ -295,7 +295,7 @@ THEOREM ProductSetZero ==
<2>. QED BY DEF P

THEOREM ProductSetNatSubset ==
ASSUME NEW S \in SUBSET Nat \ {0}, IsFiniteSet(S),
ASSUME NEW S \in SUBSET (Nat \ {0}), IsFiniteSet(S),
NEW T \in SUBSET S
PROVE ProductSet(T) <= ProductSet(S)
<1>. DEFINE U == S \ T
Expand Down Expand Up @@ -362,7 +362,7 @@ THEOREM MapThenSumSetAddElement ==
ASSUME NEW S, IsFiniteSet(S), NEW x, x \notin S,
NEW op(_), \A s \in S \union {x} : op(s) \in Int
PROVE MapThenSumSet(op, S \union {x}) = op(x) + MapThenSumSet(op, S)
<1>. \A T \in SUBSET S \union {x} : T # {} => (CHOOSE t \in T : TRUE) \in T
<1>. \A T \in SUBSET (S \union {x}) : T # {} => (CHOOSE t \in T : TRUE) \in T
OBVIOUS
<1>. /\ 0 \in Int
/\ \A i,j \in Int : i+j \in Int
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2 changes: 1 addition & 1 deletion modules/FoldsTheorems.tla
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Expand Up @@ -102,7 +102,7 @@ THEOREM MapThenFoldSetACAddElement ==
\A t,u \in Typ : op(t,u) = op(u,t),
\A t,u,v \in Typ : op(t, op(u,v)) = op(op(t,u),v),
NEW S, IsFiniteSet(S), NEW x, x \notin S,
NEW choose(_), \A T \in SUBSET S \union {x} : T # {} => choose(T) \in T,
NEW choose(_), \A T \in SUBSET (S \union {x}) : T # {} => choose(T) \in T,
\A s \in S \union {x} : f(s) \in Typ
PROVE MapThenFoldSet(op, base, f, choose, S \union {x}) =
op(f(x), MapThenFoldSet(op, base, f, choose, S))
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2 changes: 1 addition & 1 deletion modules/FoldsTheorems_proofs.tla
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Expand Up @@ -271,7 +271,7 @@ THEOREM MapThenFoldSetACAddElement ==
\A t,u \in Typ : op(t,u) = op(u,t),
\A t,u,v \in Typ : op(t, op(u,v)) = op(op(t,u),v),
NEW S, IsFiniteSet(S), NEW x, x \notin S,
NEW choose(_), \A T \in SUBSET S \union {x} : T # {} => choose(T) \in T,
NEW choose(_), \A T \in SUBSET (S \union {x}) : T # {} => choose(T) \in T,
\A s \in S \union {x} : f(s) \in Typ
PROVE MapThenFoldSet(op, base, f, choose, S \union {x}) =
op(f(x), MapThenFoldSet(op, base, f, choose, S))
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